13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- x p D p x F p lp . (15) Let us to consider two representative material volumes sur V , bulk V located near specimen surface (part of the surface volume coincides with specimen surface) and into specimen volume, respectively. If we introduce a mean defect induced strain in the considering volume as i i v m pdv v 1 p we can rewrite the equation (15) as m p m p m p F l p V hl p , (16) where we used the following boundary conditions iv p S pdv V h x p D . (17) The equation (16) requests an approximation of function p F which determined the equilibrium states of materials with defects. Taking into account the solution of equations (2) we can propose the following approximation for defect evolution law m 2 0 2 m 0 2 p m p m p p a p n E n l p V hl p , (18) where n is initial defect concentration, is mean stress for the considered volume, p ,l ,a 0 p are materials constants, h the constant which determine the boundary conditions for considered volumes. To explain the different mechanisms of crack initiation on specimen surface and in the bulk we have to consider a surface as a physical object with high concentration of incomplete atomic planes and other defect of different nature. As a result we can consider the surface as negative source with infinite capacity which has a great influence on the defect evolution. This influence can be described by the value of constant h in the boundary condition (18). There are two limiting cases for equation (18). The first case is p 0 h p S . It means the surface is the sink of infinite capacity and this condition can be used for the description of defect evolution close to specimen surface ( sur V ). The second case is 0 x p h 0 D p S . The surface is closed for the defect diffusion. This condition can be used for the description of defect evolution in the bulk of specimen ( bulk V ).
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